改进线性混合效应模型的贝叶斯推断效率，实现快速精准采样。
Hamiltonian Monte Carlo Inference of Marginalized Linear Mixed-Effects Models
- 通过自动边缘化随机效应，简化模型结构提升采样效率。
- 将传统立方时间复杂度降为线性，显著加速哈密顿蒙特卡洛采样。
- 特别适合认知科学等领域中复杂多层次数据的建模与分析。
在线性混合效应模型（LMMs）的贝叶斯推断中，通常需依赖马尔可夫链蒙特卡洛（MCMC）等高级采样技术。常见做法是将模型写入概率编程语言后，使用哈密顿蒙特卡洛（HMC）采样。然而，模型的表达方式直接影响推断效率。特别是对随机效应进行边缘化可大幅提升效率，但手动操作困难。本文提出一种算法，可自动对LMM中的随机效应进行边缘化。虽然朴素方法会引入立方时间复杂度，我们通过快速线性代数技术将其降低至线性时间。实验表明，只要适用，边缘化总是有益的，并在多个模型中取得显著性能提升，尤其在认知科学领域的应用中表现突出。
原文摘要 · Abstract (English)
Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language and then sample via Hamiltonian Monte Carlo (HMC). However, there are many ways a user can transform a model that make inference more or less efficient. In particular, marginalizing some variables can greatly improve inference but is difficult for users to do manually. We develop an algorithm to easily marginalize random effects in LMMs. A naive approach introduces cubic time operations within an inference algorithm like HMC, but we reduce the running time to linear using fast linear algebra techniques. We show that marginalization is always beneficial when applicable and highlight improvements in various models, especially ones from cognitive sciences.
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